Blockchain networks allow multiple client implementations of the same consensus algorithm by different developers to coexist in the same system. Ensuring correct implementations among these heterogeneous clients is crucial, as even slight semantic discrepancies in their implementations can lead to safety failures. While existing fuzzing frameworks have discovered implementation flaws in blockchain, they suffer from several challenges in testing them with sequences of conflicting blocks, called forks. Existing tools fail to adequately assess the fork-handling processes in blockchain implementations when relying on traditional code coverage feedback, which lacks the granularity needed to navigate the diverse and complex fork-handling scenarios. This paper introduces Forky, a fork state-aware differential fuzzing framework designed to detect implementation discrepancies within the critical fork-handling process with its novel fork-aware mutation and fork-diversifying feedback mechanisms. We test Forky on the two most influential blockchain projects: Bitcoin and Ethereum, which are the representatives of the two major blockchain consensus algorithm families, Proof-of-Work (PoW) and Proof-of-Stake (PoS) consensus algorithms.